Ive got a engineer that dispatches a team to repair them when they are damaged.

But what are they and how do I even know when they are damaged? Do I just assume that when my hull reaches a certain damage threshold that Im taking system damage? Ive never seen any of my weapons or tech go offline no matter how much damage I took so what exactly is going on with Auxiliary Damage?

the engineer repairs disabled subsystems, in this case auxiliary. So if a player or npc uses skills like "disable subsystem XXX" or phaser weapons that can do that too you can get them online again.

Auxiliary is needed for many scientific skills, they get better the higher aux, also some engineering skills (auxiliary power to ...). It also increases your turnrate and improves your sensors (when you want to detect cloaked ships), and improves your cloak (when you don't want to get detected)

Ive got a engineer that dispatches a team to repair them when they are damaged.

But what are they and how do I even know when they are damaged? Do I just assume that when my hull reaches a certain damage threshold that Im taking system damage? Ive never seen any of my weapons or tech go offline no matter how much damage I took so what exactly is going on with Auxiliary Damage?

The battery will boost your current power level in Auxiliary. Anything that's affected by your current Aux power will benefit.

The four main systems on your ship are not affected by 'normal' damage, but there are several abilities and weapon effects that can disable one or more of them temporarily. If that occurs, your engineering ability should get them up and running again.